Pub Date : 2011-09-01DOI: 10.30016/JGS.201109.0003
Xinhai Kong, Zhi-bin Liu, Yong Wei
Aiming at the discrete GM (1, 1) model (DGM (1, 1) model) can completely fit the pure exponential sequence, and according to the changing trend of the class ratio of the original sequence, this paper put forward a kind of data processing method to make the class ratio of the transformed sequence approximate the minimum or maximum class ratio of the original sequence for being better suited to construct DGM (1, 1) model. And based on the optimized DGM (1, 1) model (ODGM (1, 1) model), we construct the R-ODGM (1, 1) model and M-ODGM (1, 1) model. Examples show that this method has a good effect, and the simulation accuracy of R-ODGM (1, 1) model and M-ODGM (1, 1) model is over 98%.
{"title":"A Kind of Data Processing Method Suited to DGM (1, 1) Model","authors":"Xinhai Kong, Zhi-bin Liu, Yong Wei","doi":"10.30016/JGS.201109.0003","DOIUrl":"https://doi.org/10.30016/JGS.201109.0003","url":null,"abstract":"Aiming at the discrete GM (1, 1) model (DGM (1, 1) model) can completely fit the pure exponential sequence, and according to the changing trend of the class ratio of the original sequence, this paper put forward a kind of data processing method to make the class ratio of the transformed sequence approximate the minimum or maximum class ratio of the original sequence for being better suited to construct DGM (1, 1) model. And based on the optimized DGM (1, 1) model (ODGM (1, 1) model), we construct the R-ODGM (1, 1) model and M-ODGM (1, 1) model. Examples show that this method has a good effect, and the simulation accuracy of R-ODGM (1, 1) model and M-ODGM (1, 1) model is over 98%.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"14 1","pages":"101-106"},"PeriodicalIF":1.6,"publicationDate":"2011-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70060450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-06-01DOI: 10.30016/JGS.201106.0001
K. Huang
This study proposes a new harmonic mean (HM) GRA function based upon the harmonic mean of all attributes, and is used to enhance the applications of GRA. This study also categories all of the existing GRG models into different types basically according to the kernel function Each type has the special characteristics and limitations and is complemented to each other in the GRG ranking using GRA function. Grey relational analysis (GRA) functions provide an effective means of solving multiple-criteria decision problems by ranking the potential solutions in terms of their so-called Grey relational grades (GRGs) such that the optimal solution can be easily determined. The proposed GRA function, in which the Attribute Impulse Factors and a different formula of GRG were defined, belongs to the HM type, and could be calculated indirectly from the harmonic mean of all attributes. In mathematics, the harmonic mean is one of several kinds of average. Some illustrations were used to compare the GRG results obtained using the proposed GRA function of HM type with those of GRA functions of other types. Finally, some useful conclusions deducted from discussions.
{"title":"A New Grey Relational Analysis Function Based on Harmonic Mean","authors":"K. Huang","doi":"10.30016/JGS.201106.0001","DOIUrl":"https://doi.org/10.30016/JGS.201106.0001","url":null,"abstract":"This study proposes a new harmonic mean (HM) GRA function based upon the harmonic mean of all attributes, and is used to enhance the applications of GRA. This study also categories all of the existing GRG models into different types basically according to the kernel function Each type has the special characteristics and limitations and is complemented to each other in the GRG ranking using GRA function. Grey relational analysis (GRA) functions provide an effective means of solving multiple-criteria decision problems by ranking the potential solutions in terms of their so-called Grey relational grades (GRGs) such that the optimal solution can be easily determined. The proposed GRA function, in which the Attribute Impulse Factors and a different formula of GRG were defined, belongs to the HM type, and could be calculated indirectly from the harmonic mean of all attributes. In mathematics, the harmonic mean is one of several kinds of average. Some illustrations were used to compare the GRG results obtained using the proposed GRA function of HM type with those of GRA functions of other types. Finally, some useful conclusions deducted from discussions.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"14 1","pages":"47-54"},"PeriodicalIF":1.6,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70060078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-06-01DOI: 10.30016/JGS.201106.0002
Yuran Liu, Mao-kang Luo, Hong Ma, Mingliang Hou
In order to improve the correlation accuracy of DengShi correlation algorithm, the fractional order correlation algorithm of multiple uncertain time sequences is proposed in this paper. By taking advantage of the memory property of fractional order, the algorithm introduces the measurement of fractional order differential for the local trend of time sequence into the correlation algorithm and also analyzes the influences of differential order and noise upon correlation accuracy, provides selection relations between noise level and order. It has been proven with examples that the correlation accuracy of fractional order correlation algorithm has increased by two orders of magnitude as compared with DengShi correlation algorithm.
{"title":"Fractional Order Correlation Algorithm of Uncertain Time Sequence","authors":"Yuran Liu, Mao-kang Luo, Hong Ma, Mingliang Hou","doi":"10.30016/JGS.201106.0002","DOIUrl":"https://doi.org/10.30016/JGS.201106.0002","url":null,"abstract":"In order to improve the correlation accuracy of DengShi correlation algorithm, the fractional order correlation algorithm of multiple uncertain time sequences is proposed in this paper. By taking advantage of the memory property of fractional order, the algorithm introduces the measurement of fractional order differential for the local trend of time sequence into the correlation algorithm and also analyzes the influences of differential order and noise upon correlation accuracy, provides selection relations between noise level and order. It has been proven with examples that the correlation accuracy of fractional order correlation algorithm has increased by two orders of magnitude as compared with DengShi correlation algorithm.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"14 1","pages":"55-61"},"PeriodicalIF":1.6,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70060159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-06-01DOI: 10.30016/JGS.201106.0005
Yu-lung Hsieh, K. Linsenmair
In this paper the Verhulst Grey Model is applied to predict spider diversity dynamics in the Wurzburg University Forest, Germany. Here, we use a moving forecasting to predict the following biodiversity values: Margalef Species Richness, Fisher Alpha Index, Simpson Index and Evenness. Among these, the Fisher Alpha Index revealed a decreasing trend in the temporal dynamic across years. Our application of the model for prediction can help lower the cost of studying biodiversity patterns and provide a crucial baseline reference for improving forest management policy.
{"title":"Biodiversity Prediction by Applying Verhulst Grey Model (GM 1,1)","authors":"Yu-lung Hsieh, K. Linsenmair","doi":"10.30016/JGS.201106.0005","DOIUrl":"https://doi.org/10.30016/JGS.201106.0005","url":null,"abstract":"In this paper the Verhulst Grey Model is applied to predict spider diversity dynamics in the Wurzburg University Forest, Germany. Here, we use a moving forecasting to predict the following biodiversity values: Margalef Species Richness, Fisher Alpha Index, Simpson Index and Evenness. Among these, the Fisher Alpha Index revealed a decreasing trend in the temporal dynamic across years. Our application of the model for prediction can help lower the cost of studying biodiversity patterns and provide a crucial baseline reference for improving forest management policy.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"14 1","pages":"77-81"},"PeriodicalIF":1.6,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70060433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-06-01DOI: 10.30016/JGS.201106.0004
Zheng-xin Wang, K. Hipel, Shawei He
Grey Models are employed for simulating and forecasting the overall water supply in China, as well as a range of water uses for agriculture, industry, human consumption and ecological protection. Parameter optimization of a GM(1,1) model is formulated as a combinatorial optimization problem and is solved collectively using LINGO (a software of Operational Research). The annual data from 2001 to 2007 are used for estimating the model parameters. The data for 2008 are also included for the purpose of comparing the forecasted values to the measured observations to demonstrate the model's ability to forecast. Comparison of the simulation and forecasting results of the optimal GM(1,1) model with those of the traditional one demonstrates that the optimal algorithm is a good alternative for parameter optimization of a GM(1,1) model. The optimal GM(1,1) model is used to forecast the annual values of the various time series for the period from 2009 to 2011 based on the data from 2001 to 2008. The modeling results can assist the government in developing future policies regarding water resources management.
{"title":"Forecasting the Water Supply and Utilization in China Using Grey Model","authors":"Zheng-xin Wang, K. Hipel, Shawei He","doi":"10.30016/JGS.201106.0004","DOIUrl":"https://doi.org/10.30016/JGS.201106.0004","url":null,"abstract":"Grey Models are employed for simulating and forecasting the overall water supply in China, as well as a range of water uses for agriculture, industry, human consumption and ecological protection. Parameter optimization of a GM(1,1) model is formulated as a combinatorial optimization problem and is solved collectively using LINGO (a software of Operational Research). The annual data from 2001 to 2007 are used for estimating the model parameters. The data for 2008 are also included for the purpose of comparing the forecasted values to the measured observations to demonstrate the model's ability to forecast. Comparison of the simulation and forecasting results of the optimal GM(1,1) model with those of the traditional one demonstrates that the optimal algorithm is a good alternative for parameter optimization of a GM(1,1) model. The optimal GM(1,1) model is used to forecast the annual values of the various time series for the period from 2009 to 2011 based on the data from 2001 to 2008. The modeling results can assist the government in developing future policies regarding water resources management.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"14 1","pages":"69-76"},"PeriodicalIF":1.6,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70060393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-06-01DOI: 10.30016/JGS.201106.0003
Xiang-Ling Li, Yong Wei
Under the axiomatic system of buffer operator in grey system theory, the paper constructed some new strengthening buffer operators on the basis of inverse function .Meanwhile, the reason of some strengthening buffer operators may decrease the predicted precision is studied. A new method combined strengthening buffer operators with the optimized model that adapts to high-growth data sequence is suggested. A practical example shows the validity and feasibility of the method.
{"title":"A Kind of New Strengthening Buffer Operator and the Selection of Grey Model","authors":"Xiang-Ling Li, Yong Wei","doi":"10.30016/JGS.201106.0003","DOIUrl":"https://doi.org/10.30016/JGS.201106.0003","url":null,"abstract":"Under the axiomatic system of buffer operator in grey system theory, the paper constructed some new strengthening buffer operators on the basis of inverse function .Meanwhile, the reason of some strengthening buffer operators may decrease the predicted precision is studied. A new method combined strengthening buffer operators with the optimized model that adapts to high-growth data sequence is suggested. A practical example shows the validity and feasibility of the method.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"14 1","pages":"63-67"},"PeriodicalIF":1.6,"publicationDate":"2011-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70060222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-03-01DOI: 10.30016/JGS.201103.0002
Xin Gao, Haifei Ma
With high concentration of energy consumption industry, high oil dependence and lack of corresponding bargaining and pricing strategy, China has a high probability to be hijacked by oil price with huge fluctuations, thus oil price early-warning and risk management system is needed to reduce potential loss caused by oil price fluctuations. The primary task of early-warning is forecasting, but previous projections are all based on annual or monthly data and there is lag in forecasting and early warning results. So, in order to perceive price risk within a short time and take immediate measures, this article temporarily puts aside long-term oil price factors and analyzes oil prices in a new short-term perspective and distinct proportions, then constructs a model between oil price and factors, and forecasts volatility range of oil price through combination of Co-integration and Grey theory, and proposes oil price risk management measures in high price areas for the state and oil companies.
{"title":"International Petroleum Price Risk Early-warning Based on Grey Theory","authors":"Xin Gao, Haifei Ma","doi":"10.30016/JGS.201103.0002","DOIUrl":"https://doi.org/10.30016/JGS.201103.0002","url":null,"abstract":"With high concentration of energy consumption industry, high oil dependence and lack of corresponding bargaining and pricing strategy, China has a high probability to be hijacked by oil price with huge fluctuations, thus oil price early-warning and risk management system is needed to reduce potential loss caused by oil price fluctuations. The primary task of early-warning is forecasting, but previous projections are all based on annual or monthly data and there is lag in forecasting and early warning results. So, in order to perceive price risk within a short time and take immediate measures, this article temporarily puts aside long-term oil price factors and analyzes oil prices in a new short-term perspective and distinct proportions, then constructs a model between oil price and factors, and forecasts volatility range of oil price through combination of Co-integration and Grey theory, and proposes oil price risk management measures in high price areas for the state and oil companies.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"14 1","pages":"9-19"},"PeriodicalIF":1.6,"publicationDate":"2011-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70059903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-03-01DOI: 10.30016/JGS.201103.0005
H. Yong, Yong Wei
Based on the principle of GM (1, 1) model, firstly, this article advances the basic form of non-equigap DGM (2, 1) model. Secondly, on the assumption of getting non-equigap series' 1-AGO series by accumulating, let the prediction series obey the form of nonhomogeneous exponent, this article optimizes the grey derivative and background value of non-equigap DGM (2, 1) model by calculating the definite integral of the whitened differential equation, and then, establishes a new non-equigap DGM (2, 1) model. The new model breaks through the limitations of the non-equigap series' prediction, which only obeys homogeneous exponential law, and it improves the fitting precision and prediction precision. Furthermore, it has enlarged the application of GM (1, 1).
{"title":"The Optimization of the Non-equigap DGM (2, 1) Model","authors":"H. Yong, Yong Wei","doi":"10.30016/JGS.201103.0005","DOIUrl":"https://doi.org/10.30016/JGS.201103.0005","url":null,"abstract":"Based on the principle of GM (1, 1) model, firstly, this article advances the basic form of non-equigap DGM (2, 1) model. Secondly, on the assumption of getting non-equigap series' 1-AGO series by accumulating, let the prediction series obey the form of nonhomogeneous exponent, this article optimizes the grey derivative and background value of non-equigap DGM (2, 1) model by calculating the definite integral of the whitened differential equation, and then, establishes a new non-equigap DGM (2, 1) model. The new model breaks through the limitations of the non-equigap series' prediction, which only obeys homogeneous exponential law, and it improves the fitting precision and prediction precision. Furthermore, it has enlarged the application of GM (1, 1).","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"14 1","pages":"41-46"},"PeriodicalIF":1.6,"publicationDate":"2011-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70059572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2011-03-01DOI: 10.30016/JGS.201103.0001
J. Min, H. Tang
On July 18, 2008, Chinese tourists obtained official permits from the R.O.C. government to visit Taiwan. This policy was of historic significance, as it indicated that cross-strait relations had turned a new leaf after several turbulent decades. Due to limited data set, and changes on the economic, financial and political environment, information thus tends to be either sufficient or indefinite under such circumstances which grey theory can flexibly deal with the fuzziness situation in the current study. The main objective of this study is therefore to obtain more accurate forecasts of Chinese tourists by the GM(1,1) interval prediction model. This study lays the groundwork for future research in model building for the purpose of estimation, and the results offer useful insights for authorities, practitioners, and policymakers in the tourism industry.
{"title":"Forecasting Chinese Tourism Demand in Taiwan Using GM(1,1) Interval Prediction Model","authors":"J. Min, H. Tang","doi":"10.30016/JGS.201103.0001","DOIUrl":"https://doi.org/10.30016/JGS.201103.0001","url":null,"abstract":"On July 18, 2008, Chinese tourists obtained official permits from the R.O.C. government to visit Taiwan. This policy was of historic significance, as it indicated that cross-strait relations had turned a new leaf after several turbulent decades. Due to limited data set, and changes on the economic, financial and political environment, information thus tends to be either sufficient or indefinite under such circumstances which grey theory can flexibly deal with the fuzziness situation in the current study. The main objective of this study is therefore to obtain more accurate forecasts of Chinese tourists by the GM(1,1) interval prediction model. This study lays the groundwork for future research in model building for the purpose of estimation, and the results offer useful insights for authorities, practitioners, and policymakers in the tourism industry.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"14 1","pages":"1-7"},"PeriodicalIF":1.6,"publicationDate":"2011-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70059804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-12-01DOI: 10.30016/JGS.201012.0004
Bih-Yun Lee, Kun-Li Wen
According to the recent reports from the Department of Health, the liver disease becomes the first diseases in Taiwan. Hence, the paper mainly does an in-depth analysis on liver function diagnosis, and combines medical analysis with soft computing as our research kernel. Firstly, we select five influence factors according to the current medical analysis, in order to explore the nature of each factor, the expected input data is over 300 cases. Secondly, we make use of Nagai's method in grey system theory to convert a subjective judgment into an objective way of quantitative value, and get the mean as the output of weighting analysis. Then, the influence factors of liver function toward system's objective weighting are derived by means of GM(0,N) weighting analysis model. Besides, for complex calculation, we also develop a toolbox by using Matlab to verify our results. By the actual data and mathematic model of the subjects, we have deformed the influence factors of doctors' subjective weighting values, and have got objective weighting values for influence factor and those values are quite match with the traditional method. Thus, we can get a prototype of objective valuation of medical auxiliary platform on influence factors in liver functions.
{"title":"Apply Grey System Theory in the Weighting Analysis of Influence Factor for Liver Function","authors":"Bih-Yun Lee, Kun-Li Wen","doi":"10.30016/JGS.201012.0004","DOIUrl":"https://doi.org/10.30016/JGS.201012.0004","url":null,"abstract":"According to the recent reports from the Department of Health, the liver disease becomes the first diseases in Taiwan. Hence, the paper mainly does an in-depth analysis on liver function diagnosis, and combines medical analysis with soft computing as our research kernel. Firstly, we select five influence factors according to the current medical analysis, in order to explore the nature of each factor, the expected input data is over 300 cases. Secondly, we make use of Nagai's method in grey system theory to convert a subjective judgment into an objective way of quantitative value, and get the mean as the output of weighting analysis. Then, the influence factors of liver function toward system's objective weighting are derived by means of GM(0,N) weighting analysis model. Besides, for complex calculation, we also develop a toolbox by using Matlab to verify our results. By the actual data and mathematic model of the subjects, we have deformed the influence factors of doctors' subjective weighting values, and have got objective weighting values for influence factor and those values are quite match with the traditional method. Thus, we can get a prototype of objective valuation of medical auxiliary platform on influence factors in liver functions.","PeriodicalId":50187,"journal":{"name":"Journal of Grey System","volume":"13 1","pages":"145-152"},"PeriodicalIF":1.6,"publicationDate":"2010-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70059700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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